On the time evolution of fermionic occupation numbers

TL;DR

This paper derives an equation describing how fermionic occupation numbers evolve over time, linking their dynamics to symmetry principles, natural orbitals, and phases within the many-body wave function.

Contribution

It introduces a novel equation for the time evolution of fermionic occupation numbers in systems with more than two electrons, connecting symmetry and phase dynamics.

Findings

Derived a new equation for occupation number evolution.

Linked evolution to symmetry-adapted Pauli principles.

Connected phase dynamics to geometrical and dynamical terms.

Abstract

We derive an equation for the time evolution of the natural occupation numbers for fermionic systems with more than two electrons. The evolution of such numbers is connected with the symmetry-adapted generalized Pauli exclusion principle, as well as with the evolution of the natural orbitals and a set of many-body relative phases. We then relate the evolution of these phases to a geometrical and a dynamical term, attached to each one of the Slater determinants appearing in the configuration-interaction expansion of the wave function.